Calculator Form
Use matching corresponding sides: AB ↔ DE, BC ↔ EF, and AC ↔ DF.
Example Data Table
Sample case: Triangle B is an exact enlargement of Triangle A by a factor of 2.
| Measurement | Triangle A | Triangle B | Result |
|---|---|---|---|
| AB ↔ DE | 3 | 6 | Ratio = 2 |
| BC ↔ EF | 4 | 8 | Ratio = 2 |
| AC ↔ DF | 5 | 10 | Ratio = 2 |
| Perimeter | 12 | 24 | Perimeter scales by 2 |
| Area | 6 | 24 | Area scales by 4 |
Formula Used
For similar triangles, corresponding sides stay proportional:
DE / AB = EF / BC = DF / AC = k
If Triangle B is scaled from Triangle A:
Side in B = Side in A × kSide in A = Side in B ÷ k
Similar triangles scale perimeter exactly like side length:
Perimeter B = Perimeter A × k
Area scales with the square of the side factor:
Area B = Area A × k²
When all three sides are known, area can be verified by:
s = (a + b + c) / 2Area = √(s(s-a)(s-b)(s-c))
How to Use This Calculator
- Enter known corresponding sides for Triangle A and Triangle B.
- Keep the side order matched correctly: AB ↔ DE, BC ↔ EF, AC ↔ DF.
- Add optional perimeter or area values if you want deeper validation.
- Choose decimal places and a tolerance percentage for mismatch checks.
- Press the calculate button to show the result above the form.
- Review the solved sides, scale factor, perimeter, area factor, and warnings.
- Use the CSV or PDF buttons to export the result summary.
- Read the Plotly chart to compare side lengths and perimeters visually.
Frequently Asked Questions
1) What makes two triangles similar?
Triangles are similar when corresponding angles are equal and corresponding sides share one constant ratio. Their sizes may differ, but the overall shape remains the same.
2) Can I solve a triangle with only one side pair?
One matching side pair can establish a scale factor only when another reliable source supports it, such as perimeter ratio or area ratio. More known values give better checking.
3) What happens if my side ratios do not match?
The calculator still computes a result when possible, but it warns that the data may not represent truly similar triangles. Recheck side order and entered numbers carefully.
4) Why does area scale differently from side length?
Side lengths scale by k because they are one-dimensional. Area is two-dimensional, so it grows or shrinks by k² instead of the simple side factor.
5) Can perimeter alone prove similarity?
No. Perimeter ratio can support a known scale factor, but perimeter alone does not prove similarity. Matching angles or corresponding side ratios remain the stronger test.
6) What if all six sides are already known?
The calculator checks the three corresponding ratios, estimates the shared scale factor, and compares perimeter and area relationships. It also draws a graph for fast visual review.
7) Does the order of corresponding sides matter?
Yes. Incorrect pairing is a common mistake. Enter AB with DE, BC with EF, and AC with DF. A wrong order can make correct triangles look inconsistent.
8) Is this useful for homework and exam practice?
Yes. It helps you verify proportional reasoning, solve missing sides faster, and understand scaling effects. For school work, still show your manual steps clearly.